Graphs have long served the purpose of allowing visual perception and interpretation of data sets and functions. Typically, graphing involves plotting in two dimensions along an X and a Y axis. This involves the plotting of .[.a.]. .Iadd.an .Iaddend.X "independent" variable against .[.an.]. .Iadd.a .Iaddend.Y "dependent" variable.
There are other systems and methods for visualizing 3-D data. Such techniques include color maps, contours, wire meshes, as well as numerous other surface rendering techniques. All too often, 3-D or multi-dimensional data sets are viewed in two dimensions in the form of X,Y plots, and then repeated over various combinations until all variables are completed. Another graphing technique involves the maintenance of variables as parameters in order to produce a two dimensional X,Y plot.
Still another method of multi-dimensional graphing is referred to as a graph "matrix." This consists of plotting all points in the multi-dimensional space in terms of their projections onto all possible planes. This technique proves to be quite useful in analyzing randomly sampled data (as opposed to lattice or grid-like data), especially in statistical investigations in which a clear identification of the dependent and independent variables may not be possible. Since it is the projection of all data points onto the various planes that is shown, a variety of data "labeling" and "brushing" tools have been developed in order to identify corresponding points for each of the graphs.
These "matrix" graphs do not provide an easy and intuitive means of recognizing the mathematical form that one should use to fit multi-dimensional data. The primary reason for this shortcoming is that the matrix graph technique displays projections onto a particular two-dimensional subspace rather than all possible "parallel" planar slices through this space (corresponding to all possible values of the remaining variables).